The flybar is really nothing more than a gyroscope, and the paddles ensure that the flybar changes positions when you move around the swashplate. Technically though, the flybar is there to buffer the movement changes between the swashplate and the main blades - if the flybar wasn't there, your helicopter would be way too responsive and extremely hard to control!
The centrifugal force of the flybar's weights 'forces' the flybar to stay in a position relative to its axis of rotation. It's really not as complicated as it sounds; think about a top spinning on a desk and it's the same thing. This force is directly proportional to its rotation speed (your main motor) and the distance of the weights from the center of its axis (how far the flybar weights are from the rotor head). Pull the flybar weights out to the flybar paddles, and you end up with a pretty powerful gyroscope. Push the flybar weights toward the center, and the gyroscopic effect is greatly reduced.
So, why do we need this flybar gyroscope? Well, this is the part where PilotDane is correct. If you look closely at your helicopter's head, you'll notice that the swashplate connects directly to the flybar and not the main blade grips. You'll also notice that the main blade grips connect to the flybar. So, in effect, you really are flying the flybar! But why? Look closer... When the swashplate pitches, the flybar paddles also change pitch. But when the rotor is at full speed, the flybar itself won't immediately change pitch due to the gyroscopic effect of the flybar weights. Eventually though, the pitch of the flybar paddles will cut through the air and gently push the rotating flybar into its new position, and the main blades will simply follow along. When the main blades finally change pitch, you'll see your helicopter as it responds to your input. The time between your input and the helicopter's physical response is determined by how powerful the gyroscopic effect is of the flybar; if the weights are toward the paddles then the response time will be slow, and if the weights are toward the center then the response time will be very fast.
So, is that the flybar's only job? Not quite... You've probably noticed that the flybar 'see-saws' back and forth. And while you're hovering, you've probably noticed that your helicopter's body naturally pitches and yaws underneath the rotating blades. But did you notice that the helicopter didn't shoot off in the direction of the body's pitch or yaw? Well, that's the other job of the flybar! When the body of the helicopter swings underneath the rotor, the centrifugal force of the flybar makes sure that the helicopter's blades continue along the same track even though the helicopter's vertical axis changed angles. If the flybar wasn't there, then the helicopter would immediately fly off in the direction that the body of the helicopter pitched toward. So how does the flybar differentiate between angle changes of the helicopter's body and your intentional stick movements? The flybar paddles! Remember where I said that the paddles change pitch when the swashplate changes pitch? Well, since you didn't change the pitch of the swashplate when the helicopter's body pitched, the paddles will remain flat and the flybar will continue to track along the same path regardless of how the helicopter's body is oriented.
There's definitely a lot of technology and physics at play in these little birdies that isn't immediately evident to the naked eye... I don't know who thought up the idea of using a flybar, but it's ingenious!
